Functional regions in gravity models and accessibility measures

Accessibility measures are useful for studies in Economic Geography. For example, accessibility to potential customers can be used in a study of firm behaviour. In such a study, it would be relevant to consider where potential customers live. This can be accomplished by splitting the accessibility measure into three parts: accessibility within the municipality, in other municipalities within the functional region, and in other regions. Many studies have proved this to be a very useful way to incorporate the spatial structure of the economy into economic studies. This paper deals with the issue of finding the distance-friction parameters needed to calculate such accessibility measures. There is a particular distance-friction parameter for interaction within the municipality, between municipalities within the functional region, and between regions. One way to find the distance-friction parameters is to solve a constrained gravity model, in which the functional regions are used as constraints. Both the models and the optimisation procedures in matrix form, and the Matlab programs used in the research are presented. The spatial constraints are gradually introduced into the models, which empowers the researcher to make such adjustments on their own. The data set used is available for downloading, and the reader can then try the models before creating a data set of their own.